Be a pessimist ultimately in defeat (4)
I believe the answer is:
beat
'defeat' is the definition.
(I know that beat is a more specific form of the action defeat)
'be a pessimist ultimately' is the wordplay.
'be' becomes 'bea' (I can't explain this - if you can you should give a lot more credence to this answer).
'ultimately' says to take the final letters.
The last letter of 'pessimist' is 't'.
'bea'+'t'='BEAT'
'in' is the link.
Can you help me to learn more?
(Other definitions for beat that I've seen before include "Get the better of in competition" , "Throb; surpass" , "Master" , "Policeman's route; strike" , "Policeman's round" .)